To solve multi-step equations, follow these key steps:
Steps to Solve Multi-Step Equations
- Clear Parentheses
Use the distributive property to remove parentheses by multiplying terms inside the parentheses by the factor outside
- Combine Like Terms
Simplify each side of the equation by combining like terms (terms with the same variable or constants)
- Move Variable Terms to One Side
Use addition or subtraction to get all variable terms on one side of the equation and constants on the other side
- Isolate the Variable
Solve for the variable by performing inverse operations such as addition, subtraction, multiplication, or division. Usually, divide both sides by the coefficient of the variable to find its value
- Check Your Solution
Substitute the solution back into the original equation to verify it satisfies the equation
Additional Tips
- If the equation contains fractions, multiply every term by the least common denominator (LCD) to eliminate fractions before proceeding
- Apply the order of operations (PEMDAS) carefully when simplifying terms
Example
Solve 7(2x−1)−11=6+6x7(2x-1)-11=6+6x7(2x−1)−11=6+6x:
- Distribute 7: 14x−7−11=6+6x14x-7-11=6+6x14x−7−11=6+6x
- Combine like terms: 14x−18=6+6x14x-18=6+6x14x−18=6+6x
- Move variables left and constants right: 14x−6x=6+1814x-6x=6+1814x−6x=6+18
- Simplify: 8x=248x=248x=24
- Divide both sides by 8: x=3x=3x=3
This process illustrates the steps clearly
. Following these steps systematically will allow you to solve any multi-step linear equation effectively.
